JEE Main & Advanced Mathematics Definite Integrals Evaluation of Definite Integral by Substitution

Evaluation of Definite Integral by Substitution

Category : JEE Main & Advanced

When the variable in a definite integral is changed, the substitutions in terms of new variable should be effected at three places.

(i) In the integrand (ii)In the differential i.e., $dx$ (iii) In the limits

For example, if we put $\varphi (x)=t$ in the integral $\int_{a}^{b}{f\{\varphi (x)\}\varphi '(x)dx}$, then $\int_{a}^{b}{f\{\varphi (x)\}\varphi '(x)dx=\int_{\varphi (a)}^{\varphi (b)}{f(t)\,dt}}$.

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